Find the Solution to the Differential Equation $\frac{d^{2} s}{d t^{2}}-25 s=0$

Multiple Choice

Find the solution to the differential equation $\frac{d^{2} s}{d t^{2}}-25 s=0$ given the boundary conditions $s(0) =10$ and $s\left(\frac{s}{2}\right) =5$ .

A) $s(t) =5 \cos 25 t-10 \sin 25 t$
B) $s(t) =10 \cos 5 t+5 \sin 5 t$
C) $s(t) =10 \cos 5 t-5 \sin 5 t$
D) $s(t) =5 \cos 25 t+25 \sin 5 t$
E) $s(t) =50 \cos 5 t$